Cremona's table of elliptic curves

28224 = 2⁶ · 3² · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7-	Signs for the Atkin-Lehner involutions
Class	28224ca	Isogeny class
Conductor	28224	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-1024192512 = -1 · 212 · 36 · 73	Discriminant
Eigenvalues	2+ 3-  2 7-  4 -6  4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-84,-1568]	[a1,a2,a3,a4,a6]
Generators	[21:77:1]	Generators of the group modulo torsion
j	-64	j-invariant
L	6.4277495507904	L(r)(E,1)/r!
Ω	0.66849619028103	Real period
R	2.4038093426113	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28224cc1 14112cd1 3136m1 28224cj1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 28224ca1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	2	-	4	-6	4	-6	4	-6	-4	6	-4	-12	12	6	6	6	-12	-8	0	0	6	16	-12

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Quadratic twists for elliptic curve 28224ca1

-4	8	-3	-7
28224cc1	14112cd1	3136m1	28224cj1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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